Properties

Label 6003.2.a.t.1.6
Level 6003
Weight 2
Character 6003.1
Self dual Yes
Analytic conductor 47.934
Analytic rank 1
Dimension 22
CM No

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Newspace parameters

Level: \( N \) = \( 6003 = 3^{2} \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9341963334\)
Analytic rank: \(1\)
Dimension: \(22\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) = 6003.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.78641 q^{2} +1.19125 q^{4} -0.326188 q^{5} +1.17242 q^{7} +1.44475 q^{8} +O(q^{10})\) \(q-1.78641 q^{2} +1.19125 q^{4} -0.326188 q^{5} +1.17242 q^{7} +1.44475 q^{8} +0.582705 q^{10} +0.852209 q^{11} +3.22671 q^{13} -2.09442 q^{14} -4.96342 q^{16} +5.35744 q^{17} -1.49277 q^{19} -0.388572 q^{20} -1.52239 q^{22} +1.00000 q^{23} -4.89360 q^{25} -5.76422 q^{26} +1.39665 q^{28} +1.00000 q^{29} +0.352535 q^{31} +5.97719 q^{32} -9.57057 q^{34} -0.382430 q^{35} -10.9308 q^{37} +2.66670 q^{38} -0.471261 q^{40} -11.6880 q^{41} -3.16001 q^{43} +1.01520 q^{44} -1.78641 q^{46} +1.44410 q^{47} -5.62543 q^{49} +8.74197 q^{50} +3.84383 q^{52} +6.05996 q^{53} -0.277980 q^{55} +1.69386 q^{56} -1.78641 q^{58} +1.56212 q^{59} -6.48678 q^{61} -0.629771 q^{62} -0.750853 q^{64} -1.05251 q^{65} -6.67740 q^{67} +6.38206 q^{68} +0.683176 q^{70} -13.6764 q^{71} +12.6053 q^{73} +19.5269 q^{74} -1.77827 q^{76} +0.999148 q^{77} -15.9954 q^{79} +1.61901 q^{80} +20.8795 q^{82} -4.84681 q^{83} -1.74753 q^{85} +5.64507 q^{86} +1.23123 q^{88} -7.47777 q^{89} +3.78307 q^{91} +1.19125 q^{92} -2.57975 q^{94} +0.486925 q^{95} +3.68119 q^{97} +10.0493 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} + O(q^{10}) \) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} - 12q^{10} - 28q^{13} - q^{14} + 3q^{16} - 10q^{17} - 8q^{19} - 11q^{22} + 22q^{23} + 11q^{26} - 21q^{28} + 22q^{29} - 18q^{31} + 5q^{32} - 33q^{34} + 2q^{35} - 28q^{37} + 14q^{38} - 30q^{40} - 10q^{41} - 14q^{43} + 37q^{44} - 3q^{46} - 18q^{47} + 2q^{49} + 7q^{50} - 57q^{52} + 20q^{53} - 42q^{55} - 2q^{56} - 3q^{58} - 20q^{59} - 38q^{61} + 4q^{62} - 24q^{64} + 12q^{65} - 50q^{67} + 11q^{68} - 48q^{70} + 12q^{71} - 46q^{73} - 6q^{74} - 16q^{76} - 14q^{77} - 20q^{79} - 58q^{80} - 42q^{82} + 22q^{83} - 66q^{85} + 22q^{86} - 68q^{88} - 14q^{89} - 16q^{91} + 17q^{92} - 27q^{94} - 20q^{95} - 48q^{97} - 28q^{98} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.78641 −1.26318 −0.631590 0.775302i \(-0.717598\pi\)
−0.631590 + 0.775302i \(0.717598\pi\)
\(3\) 0 0
\(4\) 1.19125 0.595626
\(5\) −0.326188 −0.145876 −0.0729378 0.997336i \(-0.523237\pi\)
−0.0729378 + 0.997336i \(0.523237\pi\)
\(6\) 0 0
\(7\) 1.17242 0.443134 0.221567 0.975145i \(-0.428883\pi\)
0.221567 + 0.975145i \(0.428883\pi\)
\(8\) 1.44475 0.510797
\(9\) 0 0
\(10\) 0.582705 0.184267
\(11\) 0.852209 0.256951 0.128475 0.991713i \(-0.458992\pi\)
0.128475 + 0.991713i \(0.458992\pi\)
\(12\) 0 0
\(13\) 3.22671 0.894929 0.447464 0.894302i \(-0.352327\pi\)
0.447464 + 0.894302i \(0.352327\pi\)
\(14\) −2.09442 −0.559758
\(15\) 0 0
\(16\) −4.96342 −1.24086
\(17\) 5.35744 1.29937 0.649685 0.760203i \(-0.274901\pi\)
0.649685 + 0.760203i \(0.274901\pi\)
\(18\) 0 0
\(19\) −1.49277 −0.342466 −0.171233 0.985231i \(-0.554775\pi\)
−0.171233 + 0.985231i \(0.554775\pi\)
\(20\) −0.388572 −0.0868874
\(21\) 0 0
\(22\) −1.52239 −0.324575
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) −4.89360 −0.978720
\(26\) −5.76422 −1.13046
\(27\) 0 0
\(28\) 1.39665 0.263942
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) 0.352535 0.0633171 0.0316586 0.999499i \(-0.489921\pi\)
0.0316586 + 0.999499i \(0.489921\pi\)
\(32\) 5.97719 1.05663
\(33\) 0 0
\(34\) −9.57057 −1.64134
\(35\) −0.382430 −0.0646424
\(36\) 0 0
\(37\) −10.9308 −1.79702 −0.898509 0.438955i \(-0.855349\pi\)
−0.898509 + 0.438955i \(0.855349\pi\)
\(38\) 2.66670 0.432596
\(39\) 0 0
\(40\) −0.471261 −0.0745129
\(41\) −11.6880 −1.82535 −0.912677 0.408682i \(-0.865988\pi\)
−0.912677 + 0.408682i \(0.865988\pi\)
\(42\) 0 0
\(43\) −3.16001 −0.481897 −0.240948 0.970538i \(-0.577458\pi\)
−0.240948 + 0.970538i \(0.577458\pi\)
\(44\) 1.01520 0.153047
\(45\) 0 0
\(46\) −1.78641 −0.263391
\(47\) 1.44410 0.210643 0.105322 0.994438i \(-0.466413\pi\)
0.105322 + 0.994438i \(0.466413\pi\)
\(48\) 0 0
\(49\) −5.62543 −0.803632
\(50\) 8.74197 1.23630
\(51\) 0 0
\(52\) 3.84383 0.533043
\(53\) 6.05996 0.832400 0.416200 0.909273i \(-0.363362\pi\)
0.416200 + 0.909273i \(0.363362\pi\)
\(54\) 0 0
\(55\) −0.277980 −0.0374828
\(56\) 1.69386 0.226352
\(57\) 0 0
\(58\) −1.78641 −0.234567
\(59\) 1.56212 0.203370 0.101685 0.994817i \(-0.467577\pi\)
0.101685 + 0.994817i \(0.467577\pi\)
\(60\) 0 0
\(61\) −6.48678 −0.830546 −0.415273 0.909697i \(-0.636314\pi\)
−0.415273 + 0.909697i \(0.636314\pi\)
\(62\) −0.629771 −0.0799810
\(63\) 0 0
\(64\) −0.750853 −0.0938566
\(65\) −1.05251 −0.130548
\(66\) 0 0
\(67\) −6.67740 −0.815774 −0.407887 0.913032i \(-0.633734\pi\)
−0.407887 + 0.913032i \(0.633734\pi\)
\(68\) 6.38206 0.773939
\(69\) 0 0
\(70\) 0.683176 0.0816551
\(71\) −13.6764 −1.62309 −0.811545 0.584291i \(-0.801373\pi\)
−0.811545 + 0.584291i \(0.801373\pi\)
\(72\) 0 0
\(73\) 12.6053 1.47534 0.737669 0.675162i \(-0.235926\pi\)
0.737669 + 0.675162i \(0.235926\pi\)
\(74\) 19.5269 2.26996
\(75\) 0 0
\(76\) −1.77827 −0.203982
\(77\) 0.999148 0.113864
\(78\) 0 0
\(79\) −15.9954 −1.79962 −0.899809 0.436284i \(-0.856294\pi\)
−0.899809 + 0.436284i \(0.856294\pi\)
\(80\) 1.61901 0.181011
\(81\) 0 0
\(82\) 20.8795 2.30575
\(83\) −4.84681 −0.532006 −0.266003 0.963972i \(-0.585703\pi\)
−0.266003 + 0.963972i \(0.585703\pi\)
\(84\) 0 0
\(85\) −1.74753 −0.189546
\(86\) 5.64507 0.608723
\(87\) 0 0
\(88\) 1.23123 0.131250
\(89\) −7.47777 −0.792642 −0.396321 0.918112i \(-0.629713\pi\)
−0.396321 + 0.918112i \(0.629713\pi\)
\(90\) 0 0
\(91\) 3.78307 0.396573
\(92\) 1.19125 0.124197
\(93\) 0 0
\(94\) −2.57975 −0.266081
\(95\) 0.486925 0.0499574
\(96\) 0 0
\(97\) 3.68119 0.373769 0.186884 0.982382i \(-0.440161\pi\)
0.186884 + 0.982382i \(0.440161\pi\)
\(98\) 10.0493 1.01513
\(99\) 0 0
\(100\) −5.82951 −0.582951
\(101\) 9.80422 0.975556 0.487778 0.872968i \(-0.337808\pi\)
0.487778 + 0.872968i \(0.337808\pi\)
\(102\) 0 0
\(103\) −0.857878 −0.0845292 −0.0422646 0.999106i \(-0.513457\pi\)
−0.0422646 + 0.999106i \(0.513457\pi\)
\(104\) 4.66180 0.457127
\(105\) 0 0
\(106\) −10.8256 −1.05147
\(107\) 12.8882 1.24595 0.622977 0.782240i \(-0.285923\pi\)
0.622977 + 0.782240i \(0.285923\pi\)
\(108\) 0 0
\(109\) −4.06867 −0.389708 −0.194854 0.980832i \(-0.562423\pi\)
−0.194854 + 0.980832i \(0.562423\pi\)
\(110\) 0.496586 0.0473476
\(111\) 0 0
\(112\) −5.81923 −0.549865
\(113\) −5.77823 −0.543570 −0.271785 0.962358i \(-0.587614\pi\)
−0.271785 + 0.962358i \(0.587614\pi\)
\(114\) 0 0
\(115\) −0.326188 −0.0304172
\(116\) 1.19125 0.110605
\(117\) 0 0
\(118\) −2.79057 −0.256893
\(119\) 6.28118 0.575795
\(120\) 0 0
\(121\) −10.2737 −0.933976
\(122\) 11.5880 1.04913
\(123\) 0 0
\(124\) 0.419958 0.0377133
\(125\) 3.22717 0.288647
\(126\) 0 0
\(127\) 1.81622 0.161164 0.0805818 0.996748i \(-0.474322\pi\)
0.0805818 + 0.996748i \(0.474322\pi\)
\(128\) −10.6131 −0.938070
\(129\) 0 0
\(130\) 1.88022 0.164906
\(131\) −3.89276 −0.340112 −0.170056 0.985434i \(-0.554395\pi\)
−0.170056 + 0.985434i \(0.554395\pi\)
\(132\) 0 0
\(133\) −1.75016 −0.151758
\(134\) 11.9286 1.03047
\(135\) 0 0
\(136\) 7.74018 0.663715
\(137\) 3.15056 0.269171 0.134585 0.990902i \(-0.457030\pi\)
0.134585 + 0.990902i \(0.457030\pi\)
\(138\) 0 0
\(139\) −1.43304 −0.121549 −0.0607743 0.998152i \(-0.519357\pi\)
−0.0607743 + 0.998152i \(0.519357\pi\)
\(140\) −0.455570 −0.0385027
\(141\) 0 0
\(142\) 24.4316 2.05026
\(143\) 2.74983 0.229952
\(144\) 0 0
\(145\) −0.326188 −0.0270884
\(146\) −22.5182 −1.86362
\(147\) 0 0
\(148\) −13.0214 −1.07035
\(149\) −0.913677 −0.0748513 −0.0374257 0.999299i \(-0.511916\pi\)
−0.0374257 + 0.999299i \(0.511916\pi\)
\(150\) 0 0
\(151\) −16.4830 −1.34137 −0.670684 0.741743i \(-0.733999\pi\)
−0.670684 + 0.741743i \(0.733999\pi\)
\(152\) −2.15669 −0.174931
\(153\) 0 0
\(154\) −1.78489 −0.143830
\(155\) −0.114993 −0.00923643
\(156\) 0 0
\(157\) 3.94251 0.314647 0.157323 0.987547i \(-0.449713\pi\)
0.157323 + 0.987547i \(0.449713\pi\)
\(158\) 28.5742 2.27324
\(159\) 0 0
\(160\) −1.94969 −0.154136
\(161\) 1.17242 0.0923998
\(162\) 0 0
\(163\) −9.76256 −0.764663 −0.382331 0.924025i \(-0.624879\pi\)
−0.382331 + 0.924025i \(0.624879\pi\)
\(164\) −13.9233 −1.08723
\(165\) 0 0
\(166\) 8.65837 0.672020
\(167\) 21.4326 1.65851 0.829254 0.558872i \(-0.188766\pi\)
0.829254 + 0.558872i \(0.188766\pi\)
\(168\) 0 0
\(169\) −2.58834 −0.199103
\(170\) 3.12180 0.239432
\(171\) 0 0
\(172\) −3.76437 −0.287030
\(173\) −13.4151 −1.01993 −0.509967 0.860194i \(-0.670342\pi\)
−0.509967 + 0.860194i \(0.670342\pi\)
\(174\) 0 0
\(175\) −5.73737 −0.433704
\(176\) −4.22987 −0.318839
\(177\) 0 0
\(178\) 13.3583 1.00125
\(179\) 0.550115 0.0411175 0.0205588 0.999789i \(-0.493455\pi\)
0.0205588 + 0.999789i \(0.493455\pi\)
\(180\) 0 0
\(181\) 7.93736 0.589979 0.294990 0.955500i \(-0.404684\pi\)
0.294990 + 0.955500i \(0.404684\pi\)
\(182\) −6.75810 −0.500944
\(183\) 0 0
\(184\) 1.44475 0.106509
\(185\) 3.56551 0.262141
\(186\) 0 0
\(187\) 4.56566 0.333874
\(188\) 1.72029 0.125465
\(189\) 0 0
\(190\) −0.869846 −0.0631052
\(191\) 1.69390 0.122566 0.0612831 0.998120i \(-0.480481\pi\)
0.0612831 + 0.998120i \(0.480481\pi\)
\(192\) 0 0
\(193\) −2.47769 −0.178348 −0.0891741 0.996016i \(-0.528423\pi\)
−0.0891741 + 0.996016i \(0.528423\pi\)
\(194\) −6.57611 −0.472138
\(195\) 0 0
\(196\) −6.70130 −0.478664
\(197\) 0.544234 0.0387751 0.0193875 0.999812i \(-0.493828\pi\)
0.0193875 + 0.999812i \(0.493828\pi\)
\(198\) 0 0
\(199\) 6.56260 0.465211 0.232605 0.972571i \(-0.425275\pi\)
0.232605 + 0.972571i \(0.425275\pi\)
\(200\) −7.07005 −0.499928
\(201\) 0 0
\(202\) −17.5143 −1.23230
\(203\) 1.17242 0.0822879
\(204\) 0 0
\(205\) 3.81247 0.266275
\(206\) 1.53252 0.106776
\(207\) 0 0
\(208\) −16.0155 −1.11048
\(209\) −1.27215 −0.0879968
\(210\) 0 0
\(211\) −7.71720 −0.531274 −0.265637 0.964073i \(-0.585582\pi\)
−0.265637 + 0.964073i \(0.585582\pi\)
\(212\) 7.21894 0.495799
\(213\) 0 0
\(214\) −23.0237 −1.57387
\(215\) 1.03076 0.0702970
\(216\) 0 0
\(217\) 0.413320 0.0280580
\(218\) 7.26830 0.492272
\(219\) 0 0
\(220\) −0.331145 −0.0223258
\(221\) 17.2869 1.16284
\(222\) 0 0
\(223\) 11.6536 0.780386 0.390193 0.920733i \(-0.372408\pi\)
0.390193 + 0.920733i \(0.372408\pi\)
\(224\) 7.00779 0.468228
\(225\) 0 0
\(226\) 10.3223 0.686627
\(227\) 18.0449 1.19769 0.598843 0.800867i \(-0.295628\pi\)
0.598843 + 0.800867i \(0.295628\pi\)
\(228\) 0 0
\(229\) 7.11185 0.469964 0.234982 0.972000i \(-0.424497\pi\)
0.234982 + 0.972000i \(0.424497\pi\)
\(230\) 0.582705 0.0384224
\(231\) 0 0
\(232\) 1.44475 0.0948527
\(233\) −5.44024 −0.356402 −0.178201 0.983994i \(-0.557028\pi\)
−0.178201 + 0.983994i \(0.557028\pi\)
\(234\) 0 0
\(235\) −0.471048 −0.0307278
\(236\) 1.86087 0.121133
\(237\) 0 0
\(238\) −11.2207 −0.727333
\(239\) −5.34393 −0.345670 −0.172835 0.984951i \(-0.555293\pi\)
−0.172835 + 0.984951i \(0.555293\pi\)
\(240\) 0 0
\(241\) 4.78763 0.308398 0.154199 0.988040i \(-0.450720\pi\)
0.154199 + 0.988040i \(0.450720\pi\)
\(242\) 18.3531 1.17978
\(243\) 0 0
\(244\) −7.72739 −0.494695
\(245\) 1.83495 0.117230
\(246\) 0 0
\(247\) −4.81675 −0.306482
\(248\) 0.509326 0.0323422
\(249\) 0 0
\(250\) −5.76505 −0.364614
\(251\) −11.8178 −0.745934 −0.372967 0.927845i \(-0.621660\pi\)
−0.372967 + 0.927845i \(0.621660\pi\)
\(252\) 0 0
\(253\) 0.852209 0.0535779
\(254\) −3.24451 −0.203579
\(255\) 0 0
\(256\) 20.4609 1.27881
\(257\) −8.04832 −0.502041 −0.251020 0.967982i \(-0.580766\pi\)
−0.251020 + 0.967982i \(0.580766\pi\)
\(258\) 0 0
\(259\) −12.8155 −0.796319
\(260\) −1.25381 −0.0777580
\(261\) 0 0
\(262\) 6.95406 0.429623
\(263\) −8.69157 −0.535945 −0.267973 0.963427i \(-0.586354\pi\)
−0.267973 + 0.963427i \(0.586354\pi\)
\(264\) 0 0
\(265\) −1.97669 −0.121427
\(266\) 3.12650 0.191698
\(267\) 0 0
\(268\) −7.95446 −0.485896
\(269\) 13.3150 0.811829 0.405915 0.913911i \(-0.366953\pi\)
0.405915 + 0.913911i \(0.366953\pi\)
\(270\) 0 0
\(271\) 15.6543 0.950932 0.475466 0.879734i \(-0.342279\pi\)
0.475466 + 0.879734i \(0.342279\pi\)
\(272\) −26.5912 −1.61233
\(273\) 0 0
\(274\) −5.62819 −0.340011
\(275\) −4.17037 −0.251483
\(276\) 0 0
\(277\) −17.8305 −1.07133 −0.535664 0.844431i \(-0.679939\pi\)
−0.535664 + 0.844431i \(0.679939\pi\)
\(278\) 2.55999 0.153538
\(279\) 0 0
\(280\) −0.552517 −0.0330192
\(281\) 2.21112 0.131904 0.0659522 0.997823i \(-0.478992\pi\)
0.0659522 + 0.997823i \(0.478992\pi\)
\(282\) 0 0
\(283\) 7.97755 0.474216 0.237108 0.971483i \(-0.423800\pi\)
0.237108 + 0.971483i \(0.423800\pi\)
\(284\) −16.2920 −0.966754
\(285\) 0 0
\(286\) −4.91232 −0.290472
\(287\) −13.7032 −0.808876
\(288\) 0 0
\(289\) 11.7022 0.688363
\(290\) 0.582705 0.0342176
\(291\) 0 0
\(292\) 15.0161 0.878750
\(293\) 10.3091 0.602267 0.301133 0.953582i \(-0.402635\pi\)
0.301133 + 0.953582i \(0.402635\pi\)
\(294\) 0 0
\(295\) −0.509543 −0.0296667
\(296\) −15.7924 −0.917912
\(297\) 0 0
\(298\) 1.63220 0.0945508
\(299\) 3.22671 0.186606
\(300\) 0 0
\(301\) −3.70486 −0.213545
\(302\) 29.4454 1.69439
\(303\) 0 0
\(304\) 7.40926 0.424950
\(305\) 2.11591 0.121157
\(306\) 0 0
\(307\) −3.75282 −0.214185 −0.107092 0.994249i \(-0.534154\pi\)
−0.107092 + 0.994249i \(0.534154\pi\)
\(308\) 1.19024 0.0678201
\(309\) 0 0
\(310\) 0.205424 0.0116673
\(311\) −1.70068 −0.0964367 −0.0482184 0.998837i \(-0.515354\pi\)
−0.0482184 + 0.998837i \(0.515354\pi\)
\(312\) 0 0
\(313\) −28.4550 −1.60837 −0.804186 0.594378i \(-0.797398\pi\)
−0.804186 + 0.594378i \(0.797398\pi\)
\(314\) −7.04294 −0.397456
\(315\) 0 0
\(316\) −19.0545 −1.07190
\(317\) 4.71662 0.264912 0.132456 0.991189i \(-0.457714\pi\)
0.132456 + 0.991189i \(0.457714\pi\)
\(318\) 0 0
\(319\) 0.852209 0.0477145
\(320\) 0.244919 0.0136914
\(321\) 0 0
\(322\) −2.09442 −0.116718
\(323\) −7.99744 −0.444990
\(324\) 0 0
\(325\) −15.7902 −0.875885
\(326\) 17.4399 0.965908
\(327\) 0 0
\(328\) −16.8862 −0.932386
\(329\) 1.69309 0.0933432
\(330\) 0 0
\(331\) −0.172157 −0.00946260 −0.00473130 0.999989i \(-0.501506\pi\)
−0.00473130 + 0.999989i \(0.501506\pi\)
\(332\) −5.77377 −0.316877
\(333\) 0 0
\(334\) −38.2874 −2.09500
\(335\) 2.17809 0.119002
\(336\) 0 0
\(337\) 5.30625 0.289050 0.144525 0.989501i \(-0.453835\pi\)
0.144525 + 0.989501i \(0.453835\pi\)
\(338\) 4.62382 0.251503
\(339\) 0 0
\(340\) −2.08175 −0.112899
\(341\) 0.300433 0.0162694
\(342\) 0 0
\(343\) −14.8023 −0.799251
\(344\) −4.56543 −0.246152
\(345\) 0 0
\(346\) 23.9649 1.28836
\(347\) −6.97399 −0.374383 −0.187192 0.982323i \(-0.559939\pi\)
−0.187192 + 0.982323i \(0.559939\pi\)
\(348\) 0 0
\(349\) −16.2958 −0.872291 −0.436146 0.899876i \(-0.643657\pi\)
−0.436146 + 0.899876i \(0.643657\pi\)
\(350\) 10.2493 0.547847
\(351\) 0 0
\(352\) 5.09381 0.271501
\(353\) 1.29005 0.0686623 0.0343311 0.999411i \(-0.489070\pi\)
0.0343311 + 0.999411i \(0.489070\pi\)
\(354\) 0 0
\(355\) 4.46107 0.236769
\(356\) −8.90791 −0.472118
\(357\) 0 0
\(358\) −0.982729 −0.0519389
\(359\) −30.4439 −1.60677 −0.803385 0.595460i \(-0.796970\pi\)
−0.803385 + 0.595460i \(0.796970\pi\)
\(360\) 0 0
\(361\) −16.7716 −0.882717
\(362\) −14.1794 −0.745250
\(363\) 0 0
\(364\) 4.50659 0.236209
\(365\) −4.11170 −0.215216
\(366\) 0 0
\(367\) −20.3547 −1.06251 −0.531253 0.847213i \(-0.678279\pi\)
−0.531253 + 0.847213i \(0.678279\pi\)
\(368\) −4.96342 −0.258736
\(369\) 0 0
\(370\) −6.36945 −0.331132
\(371\) 7.10483 0.368864
\(372\) 0 0
\(373\) −23.7681 −1.23067 −0.615334 0.788266i \(-0.710979\pi\)
−0.615334 + 0.788266i \(0.710979\pi\)
\(374\) −8.15613 −0.421743
\(375\) 0 0
\(376\) 2.08637 0.107596
\(377\) 3.22671 0.166184
\(378\) 0 0
\(379\) 5.60685 0.288005 0.144002 0.989577i \(-0.454003\pi\)
0.144002 + 0.989577i \(0.454003\pi\)
\(380\) 0.580050 0.0297559
\(381\) 0 0
\(382\) −3.02600 −0.154823
\(383\) 34.5495 1.76540 0.882699 0.469938i \(-0.155724\pi\)
0.882699 + 0.469938i \(0.155724\pi\)
\(384\) 0 0
\(385\) −0.325910 −0.0166099
\(386\) 4.42617 0.225286
\(387\) 0 0
\(388\) 4.38523 0.222626
\(389\) −12.1605 −0.616560 −0.308280 0.951296i \(-0.599753\pi\)
−0.308280 + 0.951296i \(0.599753\pi\)
\(390\) 0 0
\(391\) 5.35744 0.270937
\(392\) −8.12735 −0.410493
\(393\) 0 0
\(394\) −0.972224 −0.0489800
\(395\) 5.21749 0.262520
\(396\) 0 0
\(397\) 14.8664 0.746122 0.373061 0.927807i \(-0.378308\pi\)
0.373061 + 0.927807i \(0.378308\pi\)
\(398\) −11.7235 −0.587645
\(399\) 0 0
\(400\) 24.2890 1.21445
\(401\) −11.9695 −0.597728 −0.298864 0.954296i \(-0.596608\pi\)
−0.298864 + 0.954296i \(0.596608\pi\)
\(402\) 0 0
\(403\) 1.13753 0.0566643
\(404\) 11.6793 0.581067
\(405\) 0 0
\(406\) −2.09442 −0.103944
\(407\) −9.31535 −0.461745
\(408\) 0 0
\(409\) 36.9672 1.82791 0.913954 0.405817i \(-0.133013\pi\)
0.913954 + 0.405817i \(0.133013\pi\)
\(410\) −6.81063 −0.336353
\(411\) 0 0
\(412\) −1.02195 −0.0503478
\(413\) 1.83146 0.0901202
\(414\) 0 0
\(415\) 1.58097 0.0776068
\(416\) 19.2867 0.945607
\(417\) 0 0
\(418\) 2.27259 0.111156
\(419\) −18.3400 −0.895969 −0.447984 0.894041i \(-0.647858\pi\)
−0.447984 + 0.894041i \(0.647858\pi\)
\(420\) 0 0
\(421\) −6.09440 −0.297023 −0.148512 0.988911i \(-0.547448\pi\)
−0.148512 + 0.988911i \(0.547448\pi\)
\(422\) 13.7861 0.671095
\(423\) 0 0
\(424\) 8.75515 0.425187
\(425\) −26.2172 −1.27172
\(426\) 0 0
\(427\) −7.60524 −0.368043
\(428\) 15.3532 0.742123
\(429\) 0 0
\(430\) −1.84135 −0.0887979
\(431\) −7.49900 −0.361214 −0.180607 0.983555i \(-0.557806\pi\)
−0.180607 + 0.983555i \(0.557806\pi\)
\(432\) 0 0
\(433\) 16.7396 0.804453 0.402226 0.915540i \(-0.368237\pi\)
0.402226 + 0.915540i \(0.368237\pi\)
\(434\) −0.738357 −0.0354423
\(435\) 0 0
\(436\) −4.84681 −0.232120
\(437\) −1.49277 −0.0714090
\(438\) 0 0
\(439\) 29.9913 1.43141 0.715704 0.698404i \(-0.246106\pi\)
0.715704 + 0.698404i \(0.246106\pi\)
\(440\) −0.401613 −0.0191461
\(441\) 0 0
\(442\) −30.8815 −1.46888
\(443\) 27.1617 1.29049 0.645245 0.763976i \(-0.276755\pi\)
0.645245 + 0.763976i \(0.276755\pi\)
\(444\) 0 0
\(445\) 2.43916 0.115627
\(446\) −20.8182 −0.985768
\(447\) 0 0
\(448\) −0.880317 −0.0415910
\(449\) 21.8977 1.03342 0.516708 0.856161i \(-0.327157\pi\)
0.516708 + 0.856161i \(0.327157\pi\)
\(450\) 0 0
\(451\) −9.96059 −0.469026
\(452\) −6.88333 −0.323764
\(453\) 0 0
\(454\) −32.2356 −1.51289
\(455\) −1.23399 −0.0578504
\(456\) 0 0
\(457\) 21.7853 1.01908 0.509538 0.860448i \(-0.329817\pi\)
0.509538 + 0.860448i \(0.329817\pi\)
\(458\) −12.7047 −0.593650
\(459\) 0 0
\(460\) −0.388572 −0.0181173
\(461\) −18.0738 −0.841781 −0.420890 0.907111i \(-0.638282\pi\)
−0.420890 + 0.907111i \(0.638282\pi\)
\(462\) 0 0
\(463\) −8.22965 −0.382464 −0.191232 0.981545i \(-0.561248\pi\)
−0.191232 + 0.981545i \(0.561248\pi\)
\(464\) −4.96342 −0.230421
\(465\) 0 0
\(466\) 9.71848 0.450200
\(467\) 25.0014 1.15693 0.578463 0.815708i \(-0.303653\pi\)
0.578463 + 0.815708i \(0.303653\pi\)
\(468\) 0 0
\(469\) −7.82873 −0.361497
\(470\) 0.841483 0.0388147
\(471\) 0 0
\(472\) 2.25687 0.103881
\(473\) −2.69299 −0.123824
\(474\) 0 0
\(475\) 7.30504 0.335178
\(476\) 7.48247 0.342959
\(477\) 0 0
\(478\) 9.54644 0.436644
\(479\) −2.60344 −0.118954 −0.0594772 0.998230i \(-0.518943\pi\)
−0.0594772 + 0.998230i \(0.518943\pi\)
\(480\) 0 0
\(481\) −35.2706 −1.60820
\(482\) −8.55265 −0.389563
\(483\) 0 0
\(484\) −12.2386 −0.556301
\(485\) −1.20076 −0.0545238
\(486\) 0 0
\(487\) 5.77061 0.261491 0.130746 0.991416i \(-0.458263\pi\)
0.130746 + 0.991416i \(0.458263\pi\)
\(488\) −9.37179 −0.424241
\(489\) 0 0
\(490\) −3.27796 −0.148083
\(491\) −26.5293 −1.19725 −0.598625 0.801030i \(-0.704286\pi\)
−0.598625 + 0.801030i \(0.704286\pi\)
\(492\) 0 0
\(493\) 5.35744 0.241287
\(494\) 8.60468 0.387143
\(495\) 0 0
\(496\) −1.74978 −0.0785674
\(497\) −16.0345 −0.719246
\(498\) 0 0
\(499\) 38.1318 1.70701 0.853507 0.521081i \(-0.174471\pi\)
0.853507 + 0.521081i \(0.174471\pi\)
\(500\) 3.84438 0.171926
\(501\) 0 0
\(502\) 21.1114 0.942250
\(503\) −9.14152 −0.407600 −0.203800 0.979013i \(-0.565329\pi\)
−0.203800 + 0.979013i \(0.565329\pi\)
\(504\) 0 0
\(505\) −3.19802 −0.142310
\(506\) −1.52239 −0.0676786
\(507\) 0 0
\(508\) 2.16358 0.0959932
\(509\) −36.4615 −1.61613 −0.808063 0.589096i \(-0.799484\pi\)
−0.808063 + 0.589096i \(0.799484\pi\)
\(510\) 0 0
\(511\) 14.7787 0.653773
\(512\) −15.3255 −0.677297
\(513\) 0 0
\(514\) 14.3776 0.634168
\(515\) 0.279829 0.0123308
\(516\) 0 0
\(517\) 1.23067 0.0541250
\(518\) 22.8938 1.00590
\(519\) 0 0
\(520\) −1.52062 −0.0666837
\(521\) 2.69985 0.118282 0.0591412 0.998250i \(-0.481164\pi\)
0.0591412 + 0.998250i \(0.481164\pi\)
\(522\) 0 0
\(523\) 32.0986 1.40358 0.701788 0.712386i \(-0.252386\pi\)
0.701788 + 0.712386i \(0.252386\pi\)
\(524\) −4.63726 −0.202580
\(525\) 0 0
\(526\) 15.5267 0.676996
\(527\) 1.88868 0.0822724
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 3.53117 0.153384
\(531\) 0 0
\(532\) −2.08488 −0.0903911
\(533\) −37.7137 −1.63356
\(534\) 0 0
\(535\) −4.20399 −0.181754
\(536\) −9.64719 −0.416695
\(537\) 0 0
\(538\) −23.7860 −1.02549
\(539\) −4.79404 −0.206494
\(540\) 0 0
\(541\) −15.4359 −0.663641 −0.331821 0.943342i \(-0.607663\pi\)
−0.331821 + 0.943342i \(0.607663\pi\)
\(542\) −27.9650 −1.20120
\(543\) 0 0
\(544\) 32.0224 1.37295
\(545\) 1.32715 0.0568489
\(546\) 0 0
\(547\) −5.05171 −0.215996 −0.107998 0.994151i \(-0.534444\pi\)
−0.107998 + 0.994151i \(0.534444\pi\)
\(548\) 3.75312 0.160325
\(549\) 0 0
\(550\) 7.44998 0.317668
\(551\) −1.49277 −0.0635943
\(552\) 0 0
\(553\) −18.7533 −0.797472
\(554\) 31.8525 1.35328
\(555\) 0 0
\(556\) −1.70711 −0.0723975
\(557\) 10.4714 0.443688 0.221844 0.975082i \(-0.428792\pi\)
0.221844 + 0.975082i \(0.428792\pi\)
\(558\) 0 0
\(559\) −10.1964 −0.431263
\(560\) 1.89816 0.0802119
\(561\) 0 0
\(562\) −3.94996 −0.166619
\(563\) −15.1161 −0.637069 −0.318535 0.947911i \(-0.603191\pi\)
−0.318535 + 0.947911i \(0.603191\pi\)
\(564\) 0 0
\(565\) 1.88479 0.0792936
\(566\) −14.2512 −0.599021
\(567\) 0 0
\(568\) −19.7590 −0.829070
\(569\) −34.2755 −1.43691 −0.718453 0.695576i \(-0.755149\pi\)
−0.718453 + 0.695576i \(0.755149\pi\)
\(570\) 0 0
\(571\) −39.8728 −1.66862 −0.834312 0.551293i \(-0.814135\pi\)
−0.834312 + 0.551293i \(0.814135\pi\)
\(572\) 3.27574 0.136966
\(573\) 0 0
\(574\) 24.4796 1.02176
\(575\) −4.89360 −0.204077
\(576\) 0 0
\(577\) −30.0528 −1.25111 −0.625556 0.780179i \(-0.715128\pi\)
−0.625556 + 0.780179i \(0.715128\pi\)
\(578\) −20.9048 −0.869527
\(579\) 0 0
\(580\) −0.388572 −0.0161346
\(581\) −5.68250 −0.235750
\(582\) 0 0
\(583\) 5.16435 0.213886
\(584\) 18.2115 0.753599
\(585\) 0 0
\(586\) −18.4163 −0.760772
\(587\) −11.6696 −0.481656 −0.240828 0.970568i \(-0.577419\pi\)
−0.240828 + 0.970568i \(0.577419\pi\)
\(588\) 0 0
\(589\) −0.526255 −0.0216839
\(590\) 0.910252 0.0374745
\(591\) 0 0
\(592\) 54.2543 2.22984
\(593\) −32.5160 −1.33527 −0.667635 0.744489i \(-0.732693\pi\)
−0.667635 + 0.744489i \(0.732693\pi\)
\(594\) 0 0
\(595\) −2.04885 −0.0839945
\(596\) −1.08842 −0.0445834
\(597\) 0 0
\(598\) −5.76422 −0.235717
\(599\) −30.3911 −1.24175 −0.620874 0.783911i \(-0.713222\pi\)
−0.620874 + 0.783911i \(0.713222\pi\)
\(600\) 0 0
\(601\) −35.2479 −1.43779 −0.718896 0.695118i \(-0.755352\pi\)
−0.718896 + 0.695118i \(0.755352\pi\)
\(602\) 6.61840 0.269746
\(603\) 0 0
\(604\) −19.6354 −0.798954
\(605\) 3.35117 0.136244
\(606\) 0 0
\(607\) −2.10437 −0.0854139 −0.0427070 0.999088i \(-0.513598\pi\)
−0.0427070 + 0.999088i \(0.513598\pi\)
\(608\) −8.92259 −0.361859
\(609\) 0 0
\(610\) −3.77987 −0.153043
\(611\) 4.65969 0.188511
\(612\) 0 0
\(613\) −16.4130 −0.662914 −0.331457 0.943470i \(-0.607540\pi\)
−0.331457 + 0.943470i \(0.607540\pi\)
\(614\) 6.70406 0.270554
\(615\) 0 0
\(616\) 1.44352 0.0581612
\(617\) 7.81267 0.314526 0.157263 0.987557i \(-0.449733\pi\)
0.157263 + 0.987557i \(0.449733\pi\)
\(618\) 0 0
\(619\) −27.8878 −1.12091 −0.560453 0.828186i \(-0.689373\pi\)
−0.560453 + 0.828186i \(0.689373\pi\)
\(620\) −0.136985 −0.00550146
\(621\) 0 0
\(622\) 3.03811 0.121817
\(623\) −8.76710 −0.351246
\(624\) 0 0
\(625\) 23.4153 0.936614
\(626\) 50.8322 2.03166
\(627\) 0 0
\(628\) 4.69653 0.187412
\(629\) −58.5613 −2.33499
\(630\) 0 0
\(631\) 19.5765 0.779330 0.389665 0.920957i \(-0.372591\pi\)
0.389665 + 0.920957i \(0.372591\pi\)
\(632\) −23.1093 −0.919240
\(633\) 0 0
\(634\) −8.42581 −0.334632
\(635\) −0.592429 −0.0235098
\(636\) 0 0
\(637\) −18.1516 −0.719194
\(638\) −1.52239 −0.0602721
\(639\) 0 0
\(640\) 3.46185 0.136842
\(641\) −9.47844 −0.374376 −0.187188 0.982324i \(-0.559937\pi\)
−0.187188 + 0.982324i \(0.559937\pi\)
\(642\) 0 0
\(643\) −4.98714 −0.196674 −0.0983368 0.995153i \(-0.531352\pi\)
−0.0983368 + 0.995153i \(0.531352\pi\)
\(644\) 1.39665 0.0550357
\(645\) 0 0
\(646\) 14.2867 0.562103
\(647\) −10.2381 −0.402501 −0.201251 0.979540i \(-0.564501\pi\)
−0.201251 + 0.979540i \(0.564501\pi\)
\(648\) 0 0
\(649\) 1.33125 0.0522561
\(650\) 28.2078 1.10640
\(651\) 0 0
\(652\) −11.6297 −0.455453
\(653\) 29.3913 1.15017 0.575086 0.818093i \(-0.304969\pi\)
0.575086 + 0.818093i \(0.304969\pi\)
\(654\) 0 0
\(655\) 1.26977 0.0496141
\(656\) 58.0123 2.26500
\(657\) 0 0
\(658\) −3.02455 −0.117909
\(659\) −37.1953 −1.44892 −0.724462 0.689315i \(-0.757912\pi\)
−0.724462 + 0.689315i \(0.757912\pi\)
\(660\) 0 0
\(661\) 7.87718 0.306387 0.153193 0.988196i \(-0.451044\pi\)
0.153193 + 0.988196i \(0.451044\pi\)
\(662\) 0.307542 0.0119530
\(663\) 0 0
\(664\) −7.00244 −0.271747
\(665\) 0.570881 0.0221378
\(666\) 0 0
\(667\) 1.00000 0.0387202
\(668\) 25.5317 0.987850
\(669\) 0 0
\(670\) −3.89095 −0.150321
\(671\) −5.52809 −0.213409
\(672\) 0 0
\(673\) 8.46069 0.326136 0.163068 0.986615i \(-0.447861\pi\)
0.163068 + 0.986615i \(0.447861\pi\)
\(674\) −9.47913 −0.365122
\(675\) 0 0
\(676\) −3.08336 −0.118591
\(677\) −0.648694 −0.0249313 −0.0124657 0.999922i \(-0.503968\pi\)
−0.0124657 + 0.999922i \(0.503968\pi\)
\(678\) 0 0
\(679\) 4.31591 0.165630
\(680\) −2.52475 −0.0968198
\(681\) 0 0
\(682\) −0.536696 −0.0205512
\(683\) 15.5457 0.594838 0.297419 0.954747i \(-0.403874\pi\)
0.297419 + 0.954747i \(0.403874\pi\)
\(684\) 0 0
\(685\) −1.02768 −0.0392655
\(686\) 26.4430 1.00960
\(687\) 0 0
\(688\) 15.6845 0.597965
\(689\) 19.5537 0.744938
\(690\) 0 0
\(691\) −17.1134 −0.651023 −0.325511 0.945538i \(-0.605536\pi\)
−0.325511 + 0.945538i \(0.605536\pi\)
\(692\) −15.9808 −0.607499
\(693\) 0 0
\(694\) 12.4584 0.472914
\(695\) 0.467439 0.0177310
\(696\) 0 0
\(697\) −62.6176 −2.37181
\(698\) 29.1109 1.10186
\(699\) 0 0
\(700\) −6.83465 −0.258326
\(701\) 16.8345 0.635829 0.317915 0.948119i \(-0.397017\pi\)
0.317915 + 0.948119i \(0.397017\pi\)
\(702\) 0 0
\(703\) 16.3173 0.615417
\(704\) −0.639884 −0.0241165
\(705\) 0 0
\(706\) −2.30455 −0.0867329
\(707\) 11.4947 0.432302
\(708\) 0 0
\(709\) −30.6600 −1.15146 −0.575730 0.817640i \(-0.695282\pi\)
−0.575730 + 0.817640i \(0.695282\pi\)
\(710\) −7.96930 −0.299082
\(711\) 0 0
\(712\) −10.8035 −0.404879
\(713\) 0.352535 0.0132025
\(714\) 0 0
\(715\) −0.896962 −0.0335445
\(716\) 0.655326 0.0244907
\(717\) 0 0
\(718\) 54.3853 2.02964
\(719\) 26.6976 0.995654 0.497827 0.867276i \(-0.334132\pi\)
0.497827 + 0.867276i \(0.334132\pi\)
\(720\) 0 0
\(721\) −1.00579 −0.0374577
\(722\) 29.9610 1.11503
\(723\) 0 0
\(724\) 9.45539 0.351407
\(725\) −4.89360 −0.181744
\(726\) 0 0
\(727\) 45.0018 1.66903 0.834513 0.550989i \(-0.185749\pi\)
0.834513 + 0.550989i \(0.185749\pi\)
\(728\) 5.46560 0.202569
\(729\) 0 0
\(730\) 7.34517 0.271857
\(731\) −16.9296 −0.626163
\(732\) 0 0
\(733\) −20.8424 −0.769833 −0.384917 0.922951i \(-0.625770\pi\)
−0.384917 + 0.922951i \(0.625770\pi\)
\(734\) 36.3618 1.34214
\(735\) 0 0
\(736\) 5.97719 0.220322
\(737\) −5.69054 −0.209614
\(738\) 0 0
\(739\) 28.5125 1.04885 0.524425 0.851457i \(-0.324280\pi\)
0.524425 + 0.851457i \(0.324280\pi\)
\(740\) 4.24742 0.156138
\(741\) 0 0
\(742\) −12.6921 −0.465943
\(743\) −22.4337 −0.823013 −0.411506 0.911407i \(-0.634997\pi\)
−0.411506 + 0.911407i \(0.634997\pi\)
\(744\) 0 0
\(745\) 0.298030 0.0109190
\(746\) 42.4596 1.55456
\(747\) 0 0
\(748\) 5.43885 0.198864
\(749\) 15.1105 0.552124
\(750\) 0 0
\(751\) 8.21818 0.299886 0.149943 0.988695i \(-0.452091\pi\)
0.149943 + 0.988695i \(0.452091\pi\)
\(752\) −7.16767 −0.261378
\(753\) 0 0
\(754\) −5.76422 −0.209921
\(755\) 5.37656 0.195673
\(756\) 0 0
\(757\) −15.6868 −0.570145 −0.285073 0.958506i \(-0.592018\pi\)
−0.285073 + 0.958506i \(0.592018\pi\)
\(758\) −10.0161 −0.363802
\(759\) 0 0
\(760\) 0.703486 0.0255181
\(761\) −16.0488 −0.581768 −0.290884 0.956758i \(-0.593949\pi\)
−0.290884 + 0.956758i \(0.593949\pi\)
\(762\) 0 0
\(763\) −4.77020 −0.172693
\(764\) 2.01786 0.0730037
\(765\) 0 0
\(766\) −61.7196 −2.23002
\(767\) 5.04049 0.182002
\(768\) 0 0
\(769\) −3.81368 −0.137525 −0.0687624 0.997633i \(-0.521905\pi\)
−0.0687624 + 0.997633i \(0.521905\pi\)
\(770\) 0.582208 0.0209813
\(771\) 0 0
\(772\) −2.95156 −0.106229
\(773\) 9.76179 0.351107 0.175554 0.984470i \(-0.443828\pi\)
0.175554 + 0.984470i \(0.443828\pi\)
\(774\) 0 0
\(775\) −1.72517 −0.0619698
\(776\) 5.31842 0.190920
\(777\) 0 0
\(778\) 21.7236 0.778827
\(779\) 17.4475 0.625121
\(780\) 0 0
\(781\) −11.6551 −0.417054
\(782\) −9.57057 −0.342243
\(783\) 0 0
\(784\) 27.9214 0.997192
\(785\) −1.28600 −0.0458993
\(786\) 0 0
\(787\) −9.60016 −0.342209 −0.171104 0.985253i \(-0.554734\pi\)
−0.171104 + 0.985253i \(0.554734\pi\)
\(788\) 0.648320 0.0230955
\(789\) 0 0
\(790\) −9.32057 −0.331611
\(791\) −6.77452 −0.240874
\(792\) 0 0
\(793\) −20.9309 −0.743280
\(794\) −26.5574 −0.942487
\(795\) 0 0
\(796\) 7.81772 0.277092
\(797\) −44.4356 −1.57399 −0.786994 0.616960i \(-0.788364\pi\)
−0.786994 + 0.616960i \(0.788364\pi\)
\(798\) 0 0
\(799\) 7.73667 0.273704
\(800\) −29.2500 −1.03414
\(801\) 0 0
\(802\) 21.3824 0.755039
\(803\) 10.7423 0.379089
\(804\) 0 0
\(805\) −0.382430 −0.0134789
\(806\) −2.03209 −0.0715773
\(807\) 0 0
\(808\) 14.1647 0.498311
\(809\) 14.6055 0.513501 0.256751 0.966478i \(-0.417348\pi\)
0.256751 + 0.966478i \(0.417348\pi\)
\(810\) 0 0
\(811\) 19.6349 0.689474 0.344737 0.938699i \(-0.387968\pi\)
0.344737 + 0.938699i \(0.387968\pi\)
\(812\) 1.39665 0.0490128
\(813\) 0 0
\(814\) 16.6410 0.583267
\(815\) 3.18443 0.111546
\(816\) 0 0
\(817\) 4.71718 0.165033
\(818\) −66.0384 −2.30898
\(819\) 0 0
\(820\) 4.54162 0.158600
\(821\) 32.1373 1.12160 0.560800 0.827952i \(-0.310494\pi\)
0.560800 + 0.827952i \(0.310494\pi\)
\(822\) 0 0
\(823\) 30.5635 1.06538 0.532689 0.846311i \(-0.321182\pi\)
0.532689 + 0.846311i \(0.321182\pi\)
\(824\) −1.23942 −0.0431773
\(825\) 0 0
\(826\) −3.27173 −0.113838
\(827\) −45.4056 −1.57891 −0.789453 0.613811i \(-0.789636\pi\)
−0.789453 + 0.613811i \(0.789636\pi\)
\(828\) 0 0
\(829\) −27.3167 −0.948747 −0.474374 0.880324i \(-0.657325\pi\)
−0.474374 + 0.880324i \(0.657325\pi\)
\(830\) −2.82426 −0.0980314
\(831\) 0 0
\(832\) −2.42279 −0.0839950
\(833\) −30.1379 −1.04422
\(834\) 0 0
\(835\) −6.99107 −0.241936
\(836\) −1.51546 −0.0524132
\(837\) 0 0
\(838\) 32.7628 1.13177
\(839\) −5.77471 −0.199365 −0.0996826 0.995019i \(-0.531783\pi\)
−0.0996826 + 0.995019i \(0.531783\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 10.8871 0.375194
\(843\) 0 0
\(844\) −9.19313 −0.316441
\(845\) 0.844284 0.0290443
\(846\) 0 0
\(847\) −12.0452 −0.413877
\(848\) −30.0781 −1.03289
\(849\) 0 0
\(850\) 46.8346 1.60641
\(851\) −10.9308 −0.374704
\(852\) 0 0
\(853\) −2.09579 −0.0717585 −0.0358792 0.999356i \(-0.511423\pi\)
−0.0358792 + 0.999356i \(0.511423\pi\)
\(854\) 13.5861 0.464905
\(855\) 0 0
\(856\) 18.6203 0.636430
\(857\) −52.3317 −1.78762 −0.893809 0.448449i \(-0.851977\pi\)
−0.893809 + 0.448449i \(0.851977\pi\)
\(858\) 0 0
\(859\) −1.34901 −0.0460277 −0.0230139 0.999735i \(-0.507326\pi\)
−0.0230139 + 0.999735i \(0.507326\pi\)
\(860\) 1.22789 0.0418708
\(861\) 0 0
\(862\) 13.3963 0.456279
\(863\) 0.664000 0.0226028 0.0113014 0.999936i \(-0.496403\pi\)
0.0113014 + 0.999936i \(0.496403\pi\)
\(864\) 0 0
\(865\) 4.37585 0.148783
\(866\) −29.9037 −1.01617
\(867\) 0 0
\(868\) 0.492368 0.0167121
\(869\) −13.6314 −0.462413
\(870\) 0 0
\(871\) −21.5460 −0.730059
\(872\) −5.87822 −0.199062
\(873\) 0 0
\(874\) 2.66670 0.0902025
\(875\) 3.78361 0.127909
\(876\) 0 0
\(877\) 14.2825 0.482285 0.241143 0.970490i \(-0.422478\pi\)
0.241143 + 0.970490i \(0.422478\pi\)
\(878\) −53.5767 −1.80813
\(879\) 0 0
\(880\) 1.37973 0.0465108
\(881\) 45.7708 1.54206 0.771028 0.636801i \(-0.219743\pi\)
0.771028 + 0.636801i \(0.219743\pi\)
\(882\) 0 0
\(883\) −37.0494 −1.24681 −0.623406 0.781898i \(-0.714252\pi\)
−0.623406 + 0.781898i \(0.714252\pi\)
\(884\) 20.5931 0.692620
\(885\) 0 0
\(886\) −48.5218 −1.63012
\(887\) −0.840415 −0.0282184 −0.0141092 0.999900i \(-0.504491\pi\)
−0.0141092 + 0.999900i \(0.504491\pi\)
\(888\) 0 0
\(889\) 2.12938 0.0714170
\(890\) −4.35733 −0.146058
\(891\) 0 0
\(892\) 13.8824 0.464818
\(893\) −2.15571 −0.0721381
\(894\) 0 0
\(895\) −0.179441 −0.00599804
\(896\) −12.4430 −0.415691
\(897\) 0 0
\(898\) −39.1182 −1.30539
\(899\) 0.352535 0.0117577
\(900\) 0 0
\(901\) 32.4659 1.08160
\(902\) 17.7937 0.592464
\(903\) 0 0
\(904\) −8.34811 −0.277654
\(905\) −2.58907 −0.0860636
\(906\) 0 0
\(907\) −12.7632 −0.423794 −0.211897 0.977292i \(-0.567964\pi\)
−0.211897 + 0.977292i \(0.567964\pi\)
\(908\) 21.4961 0.713373
\(909\) 0 0
\(910\) 2.20441 0.0730755
\(911\) 0.499026 0.0165335 0.00826674 0.999966i \(-0.497369\pi\)
0.00826674 + 0.999966i \(0.497369\pi\)
\(912\) 0 0
\(913\) −4.13049 −0.136699
\(914\) −38.9175 −1.28728
\(915\) 0 0
\(916\) 8.47201 0.279923
\(917\) −4.56396 −0.150715
\(918\) 0 0
\(919\) −5.62310 −0.185489 −0.0927445 0.995690i \(-0.529564\pi\)
−0.0927445 + 0.995690i \(0.529564\pi\)
\(920\) −0.471261 −0.0155370
\(921\) 0 0
\(922\) 32.2872 1.06332
\(923\) −44.1298 −1.45255
\(924\) 0 0
\(925\) 53.4911 1.75878
\(926\) 14.7015 0.483121
\(927\) 0 0
\(928\) 5.97719 0.196211
\(929\) 3.39932 0.111528 0.0557641 0.998444i \(-0.482241\pi\)
0.0557641 + 0.998444i \(0.482241\pi\)
\(930\) 0 0
\(931\) 8.39749 0.275217
\(932\) −6.48069 −0.212282
\(933\) 0 0
\(934\) −44.6627 −1.46141
\(935\) −1.48926 −0.0487041
\(936\) 0 0
\(937\) 34.5379 1.12830 0.564152 0.825671i \(-0.309203\pi\)
0.564152 + 0.825671i \(0.309203\pi\)
\(938\) 13.9853 0.456636
\(939\) 0 0
\(940\) −0.561136 −0.0183023
\(941\) 0.850674 0.0277312 0.0138656 0.999904i \(-0.495586\pi\)
0.0138656 + 0.999904i \(0.495586\pi\)
\(942\) 0 0
\(943\) −11.6880 −0.380613
\(944\) −7.75344 −0.252353
\(945\) 0 0
\(946\) 4.81077 0.156412
\(947\) −48.6038 −1.57941 −0.789706 0.613485i \(-0.789767\pi\)
−0.789706 + 0.613485i \(0.789767\pi\)
\(948\) 0 0
\(949\) 40.6737 1.32032
\(950\) −13.0498 −0.423391
\(951\) 0 0
\(952\) 9.07476 0.294115
\(953\) 45.2493 1.46577 0.732885 0.680353i \(-0.238173\pi\)
0.732885 + 0.680353i \(0.238173\pi\)
\(954\) 0 0
\(955\) −0.552530 −0.0178794
\(956\) −6.36597 −0.205890
\(957\) 0 0
\(958\) 4.65081 0.150261
\(959\) 3.69379 0.119279
\(960\) 0 0
\(961\) −30.8757 −0.995991
\(962\) 63.0077 2.03145
\(963\) 0 0
\(964\) 5.70327 0.183690
\(965\) 0.808193 0.0260167
\(966\) 0 0
\(967\) −27.1176 −0.872043 −0.436021 0.899936i \(-0.643613\pi\)
−0.436021 + 0.899936i \(0.643613\pi\)
\(968\) −14.8430 −0.477073
\(969\) 0 0
\(970\) 2.14505 0.0688734
\(971\) 40.2983 1.29323 0.646617 0.762815i \(-0.276183\pi\)
0.646617 + 0.762815i \(0.276183\pi\)
\(972\) 0 0
\(973\) −1.68012 −0.0538623
\(974\) −10.3087 −0.330311
\(975\) 0 0
\(976\) 32.1966 1.03059
\(977\) 43.0726 1.37801 0.689007 0.724755i \(-0.258047\pi\)
0.689007 + 0.724755i \(0.258047\pi\)
\(978\) 0 0
\(979\) −6.37262 −0.203670
\(980\) 2.18588 0.0698255
\(981\) 0 0
\(982\) 47.3921 1.51234
\(983\) −24.0627 −0.767481 −0.383740 0.923441i \(-0.625364\pi\)
−0.383740 + 0.923441i \(0.625364\pi\)
\(984\) 0 0
\(985\) −0.177523 −0.00565634
\(986\) −9.57057 −0.304789
\(987\) 0 0
\(988\) −5.73796 −0.182549
\(989\) −3.16001 −0.100482
\(990\) 0 0
\(991\) 0.202445 0.00643088 0.00321544 0.999995i \(-0.498976\pi\)
0.00321544 + 0.999995i \(0.498976\pi\)
\(992\) 2.10717 0.0669026
\(993\) 0 0
\(994\) 28.6442 0.908537
\(995\) −2.14064 −0.0678629
\(996\) 0 0
\(997\) −15.0857 −0.477770 −0.238885 0.971048i \(-0.576782\pi\)
−0.238885 + 0.971048i \(0.576782\pi\)
\(998\) −68.1190 −2.15627
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))